Logic in Argumentative Writing

Principles of Composition

Many of the important points of this section are covered in the section on writing Argumentative Essays: Being Logical. You might want to review that section first and then come back here for a more thorough review of the principles of logic.

This document is part of a collection of instructional materials used
in the Purdue University Writing Lab. The on-line version is part of OWL
(On-line Writing Lab), a project of the Purdue University Writing Lab,
funded by the School of Liberal Arts at Purdue.

We use logic every day to figure out test questions, plan our
budgets, and decide who to date. We borrow from the vocabulary of logic
when we say, "Brilliant deduction" or even "I don't want
to argue about it." In the study of logic, however, each of these
terms has a specific definition, and we must be clear on these if we are
to communicate.

Vocabulary

Proposition --

T or F in an argument, but not alone. Can be a premise or conclusion.
Is not equal to a sentence.

Premise --

Proposition used as evidence in an argument.

Conclusion --

Proposition used as a thesis in an argument.

Argument --

A group of propositions of which one is claimed to follow from the
others.

Induction --

A process through which the premises provide some basis for the conclusion

Deduction --

A process through which the premises provide conclusive proof for the
conclusion.

Argument Indicators:

Premise Indicators:

Conclusion Indicators:

should

must

ought

necessarily

since

because

for

as

inasmuch as

for the reason that

first ...

therefore

hence

thus

so

consequently

it follows that

one may infer

one may conclude

When dealing with persuasive writing, it will be helpful for you to
outline the argument by premises and conclusions. By looking at the structure
of the argument, it is easy to spot logical error.

Example 1

"Universities are full of knowledge. The freshmen bring a little
in, and the seniors take none away, and knowledge accumulates.

-- Harvard President A. L. Lowell

Premise 1
Premise 2
Premise 3
Conclusion

Freshmen bring a little (knowledge) in
Seniors take none away
Knowledge accumulates
Universities are full of knowledge

Example 2

(Here, the conclusion of one argument is used as a premise in another.
This is very common.)

Even though there may be a deceiver of some sort, very powerful and
very tricky, who bends all his efforts to keep me perpetually deceived,
there can be no slightest doubt that I exist, since he deceives me; and
let him deceive me as much as he will, he can never make me be nothing
as long as I think I am something. Thus, after having thought well on this
matter, and after examining all things with care, I must finally conclude
and maintain that this proposition: I am, I exist, is necessarily true
every time that I pronounce it or conceive it in my mind.

-- Rene Descartes, *Meditations*

Argument 1 Premise 1:

Conclusion of Argument 1
Argument 2 Premise 1:

Conclusion:

To be deceived ... I must exist

When I think that I exist I cannot be
deceived about that

I am, I exist, is necessarily true ... .

Exercises

Find the Arguments and Outline them in These Statements:

1. Ask the same for me, for friends should have all things in common.

-- Plato, Phaedrus

2. Matter is activity, and therefore a body is where it acts; and because
every particle of matter acts all over the universe, every body is everywhere.

Reaching Logical Conclusions

This article is reprinted from pages 78-79 of Pearson-Allen:
Modern Algebra , Book One. In the book it is one of several between-chapter
articles that add interest and provike thought on subjects related to the
topics discussed in the text.

Consider the two statements:

1. Any member of a varsity squad is excused from physical education.
2. Henry is a member of the varsity football squad.

Our common sense tells us that if we accept these two statement as true,
then we must accept the following third statement as true:

3. Henry is excused from physical education.

We say that the third statement follows logically from the other
two.

In drawing logical conclusions it does not matter whether the statements
we accept as true are reasonable or sensible. This is because we depend
entirely upon the form of the statements and not upon what we are talking
about. Thus, if we accept the following statements as true:

1. All whales are mammals;
2. All mammals are warm-blooded animals;
3. All warm-blooded animals are subject to colds;

then we must conclude that

4. All whales are subject to colds. Do you see that statements 1, 2,
and 3 are arranged in logical order ?

In the diagram at the right the set of whales is represented
by W, the set of mammals by M, the set of warm-blooded
animals by B, the set of animals by B, the set of animals
subject to colds by C, and the set of all animals by A. The
diagram shows that W is a subset of M as required by
statement 1, that M is a subset of B as required by statement
2, and that B is a subset of C as required by statement 3. The
only conclusion that uses all of our given statements is that
W is a subset of C, as asserted by statement 4.

Had our third statement been "no warm-blooded animals are subject
to colds," our diagram would have been the one shown at the right
and our conclusion would have been "no whales are subject to colds."

If you have read Alice's Adventures in Wonderland or Through
the Looking-Glass , you know that their author, Lewis Carroll, delighted
in giving sets of nonsense statements which lead to logical conclusions.
One such set is the following:

Babies are illogical;

Nobody is despised who can manage a crocodile;

Illogical persons are despised.

When these statements are arranged in logical order we have:

1. Babies are illogical;
2. Illogical persons are despised;
3. Nobody is despised who can manage a crocodile.

From these we can draw the logical conclusion:

4. Babies cannot manage crocodiles.

Other sets of statements written by this author follow. To draw a conclusion
from each set of statements, first arrange the statements in logical order.
A diagram such as those in the preceding column may help you. The correct
conclusions are given at the bottom of the page, but do not look at them
until you have written your conclusion.

I.

1. Everyone who is sane can do Logic;
2. No lunatics are fit to serve on a jury;
3. None of your sons can do Logic.

1. No kitten that loves fish is unteachable;
2. No kitten without a tail will play with a gorilla;
3. Kittens with whiskers always love fish;
4. No teachable kitten has green eyes;
5. No kittens have tails unless they have whiskers.

IV.

1. There is no box of mine here that I dare open;
2. My writing-desk is a box made of rose-wood;
3. All my boxes are painted except what are here;
4. There is no box of mine that I dare not open, unless
it is full of live scorpions;
5. All my rose-wood boxes are unpainted.

Conclusions:

I. None of your sons are fit to serve on the jury.
II. My poultry are not officers.
III. No kitten with green eyes will play with a gorilla.
IV. My writing-desk is full of live scorpions.

With this brief introduction to Lewis Carroll type problems, you will
find it worthwhile and interesting to construct your own problems of this
type.

Fallacies

(The fun part)

A fallacy is an error of reasoning. It can be used against you
in an argument, but if you are familiar with them, you will be able to
refute the fallacious argument. Likewise, if you are clever, you can use
them to convince others.

Fallacies fall into two major categories:

Fallacies of Relevance

-- Premises are irrelevant to the conclusion.

Fallacies of Ambiguity

-- Ambiguous, changeable wording in the propositions

Here are examples of each of the major fallacies. You figure out and
write in a definition which makes sense to you.

Fallacies of Relevance

1. Argumentum ad Bacculum (appeal to force) --

"Pay back the loan and 10 % daily interest by Thursday, or be
sure that you have you hospital insurance paid up."

"It's time to come in the house now, Billy."
"Why?"
"Because I said so!"
"Why?"
"Because it's time, and I said so."

12. Complex Question --

"Have you given up cheating on exams?"

13. Ignoratio Elenchi (irrelevant conclusion) --

In a law court, in attempt to prove that the accused is guilty of theft,
the prosecution may argue that theft is a horrible crime for anyone to
commit.

Fallacies of Ambiguity

1. Equivocation --

Some dogs have fuzzy ears. My dog has fuzzy ears. My dog is some dog!

2. Amphibole (grammatical construction) --

"Woman without her man would be lost." or "Save Soap
and Waste Paper."

3. Accent --

"We should not speak ill of our friends."

4. Composition--

"Each part of this stereo weighs under one pound. This is a very
light stereo."
or " ... ONLY $1.97 plus processing and postage."

5. Division--

"Purdue is a great engineering school. Mike went there; he must
be a great engineer."

Listen to your roommate, the T.V., and even your profs. You'll be amazed
how many fallacies we encounter each day.

More important, check your papers. Does your argument have premisses
and conclusions stated properly? Have you been guilty of fallacious reasoning?

Exercises 1-11

(from Copi, Introduction to Logic pp. 85-87)

Identify the Fallacies in the Following Passages and Explain how each
Specific Passage Involves that Fallacy or Fallacies:

1. It is necessary to confine criminals and to lock up dangerous lunatics.
Therefore there is nothing wrong with depriving people of their liberties.

2. How much longer are you going to waste your time in school when you
might be doing a man's work in the world, and contributing to society?
If you had any sense of social responsibility, you would leave immediately.

3. The army is notoriously inefficient, so we cannot expect Major Smith
to do an efficient job.

4. God exists because the Bible tells us so, and we know that what the
Bible tells us must be true because it is the revealed word of God.

5. Congress shouldn't bother to consult the Joint Chiefs-of-Staff about
the military appropriations. As members of the armed forces, they will
naturally want as much money for military purposes as they think they can
get.

6. Mr. Brown: I will give no more money to your cause next year.
Solicitor: That's all right, sir, we'll just put you down for the same
amount that you gave this year.

7. When we had got to this point in the argument, and every one saw
that the definition of justice had been completely upset, Thrasymachus,
instead of replying to me, said:

"Tell me, Socrates, have you got a nurse?"
"Why do you ask such a question," I said, "when you ought
rather to be answering?"
"Because she leaves you to snivel, and never wipes your nose: she
has not even taught you to know the shepherd from the sheep."

-- Plato, Republic

8. Narcotics are habit-forming. Therefore if you allow your physician
to ease your pain with an opiate, you will become a hopeless drug addict.

9. You can't prove that he was to blame for the misfortune, so it must
actually have been someone else who was responsible.

10. You can't park here. I don't care what the sign says. If you don't
drive on, I'll give you a ticket.

11. But lest you think, that my piety has here got the better of my
philosophy, I shall support my opinion, if it needs my support, by a very
great authority. I might cite all the divines almost, from the foundation
of Christianity, who have ever treated of this or any other theological
subjects: but I shall confine myself, at present, to one equally celebrated
for piety and philosophy. It is Father Malebranche...

-- David Hume, Dialogues Concerning Natural Religion

Exercises 16-30

(from Copi, *Introduction to Logic* pp. 87-88)

16. Cooks have been preparing food for generations, so our cook must
be a real expert.

17. More young people are attending high schools and colleges than ever
before in the history of our nation. But there is more juvenile delinquency
than ever before. This makes it clear that to eliminate delinquency among
the youth we must abolish the schools.

18. You say we ought to discuss whether or not to buy a new car now.
All right, I agree. Let's discuss the matter. Which should we get, a Ford
or a Chevy?

19. Our nation is a democracy and dedicated to the proposition that
all men are created equal. We believe in equality of opportunity for everyone,
so our colleges and universities should admit every applicant, regardless
of his economic or educational background.

20. Anyone who deliberately strikes another person should be punished.
Therefore the middleweight boxing champion should be severely punished,
for he assaults all of his opponents.

21. We should reject Mr. Watkins' suggestions for increasing the efficiency
of our colleges. As a manufacturer he cannot be expected to realize that
our aim is to educate the youth, not to make a profit. His recommendations
can have no value for us.

22. Everyone said that the soup had a very distinctive taste, so they
must all have found it very tasty.

23. If we want to know whether a state is brave we must look at its
army, not because the soldiers are the only brave people in the community,
but because it is only through their conduct that the courage or cowardice
of the community can be manifested.

-- R. L. Nettleship, Lectures on the Republic
of Plato

24. My client is the sole support of his aged parents. If he is sent
to prison, it will break their hearts, and they will be left homeless and
penniless. You surely cannot find it in your hearts to reach any other
verdict than "not guilty."

25. There is no proof that the secretary "leaked" the news
to the papers, so she can't have done it.

26. Diamonds are seldom found in this country, so you must be careful
not to mislay your engagement ring.

27. Was it through stupidity of through deliberate dishonesty that the
Administration has hopelessly botched its foreign policy? In either case,
unless you are in favor of stupidity or dishonesty, you should vote against
the incumbents.

28. Since all men are mortal, the human race must some day come to an
end.

Try these for Fun!

Exercises in Reasoning

I. Four men, whom we shall call Robert, Ralph, Ronald, and Rudolph,
were playing cards one evening. As a result of a quarrel during the course
of the game, one of these men shot and killed another. From the facts below
determine the murder and the victim.

Rudolph had known Ronald for only five days prior to the murder.

Robert will not expose his brother's guilt.

Rudolph has been released from jail on the day of the murder, after
serving a three day sentence.

Ralph met Robert's father only once.

Robert had wheeled Ralph, a cripple, to the card game at Ronald's home.

The host is about to give evidence against the murderer, whom he dislikes.

The murdered man had eaten dinner on the previous evening with one
of the men who did not customarily bowl with Ronald.

II. Five men are in a poker game: Brown, Perkins, Turner, Jones,
and Reilly. Their brands of cigarettes are Luckies, Camels, Kools, Old
Golds, and Chesterfields, but not necessarily in that order. At the beginning
of the game, the number of cigarettes possessed by each player was 20,
15, 8, 6, and 3, but not necessarily in that order.

During the game, at a certain time when no one was smoking, the following
obtained:

Perkins asked for three cards.

Reilly had smoked half of his original supply, or one less than Turner
had smoked.

The Chesterfield man originally had as many more, plus half as many
more, plus 2 1/2 more cigarettes than he has now.

The man who was drawing to an inside straight could taste only the
menthol in his fifth cigarette, the last one he smoked.

The man who smokes Luckies had smoked at least two more than anyone
else, including Perkins.

Brown drew as many aces as he originally had cigarettes.

No one had smoked all his cigarettes.

The Camel man asks Jones to pass Brown's matches.

How many cigarettes did each man have to begin with, and of what brand?

Improprieties

A functional impropriety is the use of a word as the wrong part of speech.
The wrong meaning for a word can also be impropriety.

Mark improprieties in the following phrases and correct them in the
blanks at the right. If you find none, write C in the blank. Example: (occupation)
hazards -- occupational

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prohibited. Portions of this document may be copyrighted by other organizations.

This document is part of a collection of instructional materials used
in the Purdue University Writing Lab. The on-line version is part of OWL
(On-line Writing Lab), a project of the Purdue University Writing Lab,
funded by the School of Liberal Arts at Purdue.